MinT - Best Known (249−117, 249, s)-Nets in Base 4

Best Known (249−117, 249, s)-Nets in Base 4

(249−117, 249, 130)-Net over F₄ — Constructive and digital

Digital (132, 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]

(249−117, 249, 212)-Net over F₄ — Digital

Digital (132, 249, 212)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−117, 249, 2760)-Net in Base 4 — Upper bound on s

There is no (132, 249, 2761)-net in base 4, because

1 times m-reduction [i] would yield (132, 248, 2761)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 205873 105199 325396 519863 614942 435805 493760 580957 120318 464332 709305 327030 005082 150957 191625 144780 088669 657108 287590 724249 702352 312593 503600 161884 287200 > 4²⁴⁸ [i]