MinT - Best Known (249−113, 249, s)-Nets in Base 4

Best Known (249−113, 249, s)-Nets in Base 4

(249−113, 249, 130)-Net over F₄ — Constructive and digital

Digital (136, 249, 130)-net over F₄, using

t-expansion [i] based on digital (105, 249, 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]

(249−113, 249, 237)-Net over F₄ — Digital

Digital (136, 249, 237)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−113, 249, 3309)-Net in Base 4 — Upper bound on s

There is no (136, 249, 3310)-net in base 4, because

1 times m-reduction [i] would yield (136, 248, 3310)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 205310 712928 793102 291370 014607 887333 578045 075458 880646 380332 090820 765848 948990 006256 680482 240212 383840 772544 840494 679209 430307 214258 691046 552721 676116 > 4²⁴⁸ [i]