MinT - Best Known (196−77, 196, s)-Nets in Base 4

Best Known (196−77, 196, s)-Nets in Base 4

(196−77, 196, 130)-Net over F₄ — Constructive and digital

Digital (119, 196, 130)-net over F₄, using

t-expansion [i] based on digital (105, 196, 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]

(196−77, 196, 305)-Net over F₄ — Digital

Digital (119, 196, 305)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−77, 196, 6123)-Net in Base 4 — Upper bound on s

There is no (119, 196, 6124)-net in base 4, because

1 times m-reduction [i] would yield (119, 195, 6124)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2529 521666 015850 433645 488559 876017 429408 785712 715083 250262 189298 244357 057433 987271 483607 881125 813876 042807 989375 724482 > 4¹⁹⁵ [i]