MinT - Best Known (151−70, 151, s)-Nets in Base 4

Best Known (151−70, 151, s)-Nets in Base 4

(151−70, 151, 104)-Net over F₄ — Constructive and digital

Digital (81, 151, 104)-net over F₄, using

t-expansion [i] based on digital (73, 151, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(151−70, 151, 143)-Net over F₄ — Digital

Digital (81, 151, 143)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(151−70, 151, 1806)-Net in Base 4 — Upper bound on s

There is no (81, 151, 1807)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 248664 317340 836442 644461 999233 402915 872104 909020 506018 625342 446608 538858 640144 631738 329920 > 4¹⁵¹ [i]