MinT - Best Known (53, 53+35, s)-Nets in Base 4

Best Known (53, 53+35, s)-Nets in Base 4

(53, 53+35, 130)-Net over F₄ — Constructive and digital

Digital (53, 88, 130)-net over F₄, using

6 times m-reduction [i] based on digital (53, 94, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 47, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(53, 53+35, 152)-Net over F₄ — Digital

Digital (53, 88, 152)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+35, 2870)-Net in Base 4 — Upper bound on s

There is no (53, 88, 2871)-net in base 4, because

1 times m-reduction [i] would yield (53, 87, 2871)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 24074 346511 805846 708532 071500 581060 215675 209343 209906 > 4⁸⁷ [i]