MinT - Best Known (125, 232, s)-Nets in Base 4

Best Known (125, 232, s)-Nets in Base 4

(125, 232, 130)-Net over F₄ — Constructive and digital

Digital (125, 232, 130)-net over F₄, using

t-expansion [i] based on digital (105, 232, 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]

(125, 232, 211)-Net over F₄ — Digital

Digital (125, 232, 211)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(125, 232, 2845)-Net in Base 4 — Upper bound on s

There is no (125, 232, 2846)-net in base 4, because

1 times m-reduction [i] would yield (125, 231, 2846)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 007102 232183 387483 724736 105298 003475 807981 034296 567052 041013 232866 738537 542392 239114 424897 221471 134580 764839 686562 892759 437379 654592 318600 > 4²³¹ [i]