MinT - Best Known (58, 58+78, s)-Nets in Base 4

Best Known (58, 58+78, s)-Nets in Base 4

(58, 58+78, 66)-Net over F₄ — Constructive and digital

Digital (58, 136, 66)-net over F₄, using

t-expansion [i] based on digital (49, 136, 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]

(58, 58+78, 91)-Net over F₄ — Digital

Digital (58, 136, 91)-net over F₄, using

t-expansion [i] based on digital (50, 136, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(58, 58+78, 613)-Net in Base 4 — Upper bound on s

There is no (58, 136, 614)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7614 831295 209143 460995 340612 442316 175871 352082 570563 479882 086622 809468 196196 608432 > 4¹³⁶ [i]