MinT - Best Known (246−125, 246, s)-Nets in Base 4

Best Known (246−125, 246, s)-Nets in Base 4

(246−125, 246, 130)-Net over F₄ — Constructive and digital

Digital (121, 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]

(246−125, 246, 168)-Net over F₄ — Digital

Digital (121, 246, 168)-net over F₄, using

t-expansion [i] based on digital (115, 246, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(246−125, 246, 1859)-Net in Base 4 — Upper bound on s

There is no (121, 246, 1860)-net in base 4, because

1 times m-reduction [i] would yield (121, 245, 1860)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3287 445840 775257 656861 363829 066307 705538 766970 947116 689580 286993 194453 359956 621938 386489 530108 044768 825792 818070 568580 773393 386163 613091 198130 146800 > 4²⁴⁵ [i]