MinT - Best Known (119, 119+137, s)-Nets in Base 4

Best Known (119, 119+137, s)-Nets in Base 4

(119, 119+137, 130)-Net over F₄ — Constructive and digital

Digital (119, 256, 130)-net over F₄, using

t-expansion [i] based on digital (105, 256, 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]

(119, 119+137, 168)-Net over F₄ — Digital

Digital (119, 256, 168)-net over F₄, using

t-expansion [i] based on digital (115, 256, 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]

(119, 119+137, 1522)-Net in Base 4 — Upper bound on s

There is no (119, 256, 1523)-net in base 4, because

1 times m-reduction [i] would yield (119, 255, 1523)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3379 696783 435916 935043 507731 004393 762314 726333 778318 340012 514849 602536 199423 481029 982330 136863 318061 986203 011203 025150 001509 308820 039417 513394 351244 473820 > 4²⁵⁵ [i]