MinT - Best Known (77−64, 77, s)-Nets in Base 32

Best Known (77−64, 77, s)-Nets in Base 32

(77−64, 77, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 77, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 77, 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]

(77−64, 77, 129)-Net over F₃₂ — Digital

Digital (13, 77, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 77, 129)-net over F₃₂, using
- net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(77−64, 77, 1710)-Net in Base 32 — Upper bound on s

There is no (13, 77, 1711)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 79 572831 761854 410118 242002 472984 545908 996839 945858 768110 241554 388902 239004 620553 832352 685202 115071 840256 294351 127665 > 32⁷⁷ [i]