MinT - Best Known (259−119, 259, s)-Nets in Base 4

Best Known (259−119, 259, s)-Nets in Base 4

(259−119, 259, 130)-Net over F₄ — Constructive and digital

Digital (140, 259, 130)-net over F₄, using

t-expansion [i] based on digital (105, 259, 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]

(259−119, 259, 236)-Net over F₄ — Digital

Digital (140, 259, 236)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−119, 259, 3217)-Net in Base 4 — Upper bound on s

There is no (140, 259, 3218)-net in base 4, because

1 times m-reduction [i] would yield (140, 258, 3218)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 217850 168951 095662 012876 375186 626248 890747 975205 342246 426369 106598 901438 433058 798408 098746 982672 283710 446650 065925 883158 300491 228747 596006 795216 412331 298240 > 4²⁵⁸ [i]