MinT - Best Known (59, 59+54, s)-Nets in Base 4

Best Known (59, 59+54, s)-Nets in Base 4

(59, 59+54, 66)-Net over F₄ — Constructive and digital

Digital (59, 113, 66)-net over F₄, using

t-expansion [i] based on digital (49, 113, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(59, 59+54, 102)-Net over F₄ — Digital

Digital (59, 113, 102)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+54, 1183)-Net in Base 4 — Upper bound on s

There is no (59, 113, 1184)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 109 693300 044965 441473 676591 937482 001598 171024 840447 665173 319328 339375 > 4¹¹³ [i]