MinT - Best Known (236−105, 236, s)-Nets in Base 4

Best Known (236−105, 236, s)-Nets in Base 4

(236−105, 236, 130)-Net over F₄ — Constructive and digital

Digital (131, 236, 130)-net over F₄, using

t-expansion [i] based on digital (105, 236, 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]

(236−105, 236, 240)-Net over F₄ — Digital

Digital (131, 236, 240)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−105, 236, 3502)-Net in Base 4 — Upper bound on s

There is no (131, 236, 3503)-net in base 4, because

1 times m-reduction [i] would yield (131, 235, 3503)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3074 373693 677059 304829 506249 015501 393465 181344 020997 897554 471454 906677 870101 759645 591606 173281 624110 665665 590352 832344 731627 480104 403753 152488 > 4²³⁵ [i]