MinT - Best Known (196−79, 196, s)-Nets in Base 4

Best Known (196−79, 196, s)-Nets in Base 4

(196−79, 196, 130)-Net over F₄ — Constructive and digital

Digital (117, 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]

(196−79, 196, 280)-Net over F₄ — Digital

Digital (117, 196, 280)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−79, 196, 5223)-Net in Base 4 — Upper bound on s

There is no (117, 196, 5224)-net in base 4, because

1 times m-reduction [i] would yield (117, 195, 5224)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2531 994716 118842 604787 350141 715451 765067 390778 609149 662300 860438 581652 962283 512786 712670 705426 903721 739724 662624 720417 > 4¹⁹⁵ [i]