MinT - Best Known (54, 54+54, s)-Nets in Base 32

Best Known (54, 54+54, s)-Nets in Base 32

(54, 54+54, 240)-Net over F₃₂ — Constructive and digital

Digital (54, 108, 240)-net over F₃₂, using

t-expansion [i] based on digital (51, 108, 240)-net over F₃₂, using
- 1 times m-reduction [i] based on digital (51, 109, 240)-net over F₃₂, using
  - (u,Â u+v)-construction [i] based on
    1. digital (11, 40, 120)-net over F₃₂, using
      - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]
    2. digital (11, 69, 120)-net over F₃₂, using
      - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(54, 54+54, 513)-Net in Base 32 — Constructive

(54, 108, 513)-net in base 32, using

t-expansion [i] based on (46, 108, 513)-net in base 32, using
- base change [i] based on digital (28, 90, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(54, 54+54, 792)-Net over F₃₂ — Digital

Digital (54, 108, 792)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+54, 369512)-Net in Base 32 — Upper bound on s

There is no (54, 108, 369513)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 599362 621302 096234 520974 973672 105027 485792 639541 059915 826546 836075 134514 206112 494687 059681 142019 390251 638733 306613 706541 998680 029925 465101 227052 920164 034944 718816 > 32¹⁰⁸ [i]