MinT - Best Known (256−118, 256, s)-Nets in Base 4

Best Known (256−118, 256, s)-Nets in Base 4

(256−118, 256, 130)-Net over F₄ — Constructive and digital

Digital (138, 256, 130)-net over F₄, using

t-expansion [i] based on digital (105, 256, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(256−118, 256, 231)-Net over F₄ — Digital

Digital (138, 256, 231)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−118, 256, 3067)-Net in Base 4 — Upper bound on s

There is no (138, 256, 3068)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13598 554245 924391 887100 611812 869184 365158 255974 789384 160674 085532 886296 657641 051296 900518 967065 998861 509291 230145 724235 087684 359760 543610 016975 319526 874049 > 4²⁵⁶ [i]