MinT - Best Known (131, 131+103, s)-Nets in Base 4

Best Known (131, 131+103, s)-Nets in Base 4

(131, 131+103, 130)-Net over F₄ — Constructive and digital

Digital (131, 234, 130)-net over F₄, using

t-expansion [i] based on digital (105, 234, 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]

(131, 131+103, 247)-Net over F₄ — Digital

Digital (131, 234, 247)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+103, 3684)-Net in Base 4 — Upper bound on s

There is no (131, 234, 3685)-net in base 4, because

1 times m-reduction [i] would yield (131, 233, 3685)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190 896563 017783 724040 605652 498227 310550 372535 541781 129455 917883 960797 044408 340478 716344 437343 401495 611211 044146 928722 042177 470259 402876 230448 > 4²³³ [i]