MinT - Best Known (127, 246, s)-Nets in Base 4

Best Known (127, 246, s)-Nets in Base 4

(127, 246, 130)-Net over F₄ — Constructive and digital

Digital (127, 246, 130)-net over F₄, using

t-expansion [i] based on digital (105, 246, 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]

(127, 246, 192)-Net over F₄ — Digital

Digital (127, 246, 192)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 246, 2357)-Net in Base 4 — Upper bound on s

There is no (127, 246, 2358)-net in base 4, because

1 times m-reduction [i] would yield (127, 245, 2358)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3218 903641 089725 361669 031976 695164 754179 578978 900169 598962 396079 678897 772344 052162 354910 188827 741419 509065 840499 475302 066590 719060 100308 011403 927232 > 4²⁴⁵ [i]