MinT - Best Known (260−141, 260, s)-Nets in Base 4

Best Known (260−141, 260, s)-Nets in Base 4

(260−141, 260, 130)-Net over F₄ — Constructive and digital

Digital (119, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 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]

(260−141, 260, 168)-Net over F₄ — Digital

Digital (119, 260, 168)-net over F₄, using

t-expansion [i] based on digital (115, 260, 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]

(260−141, 260, 1457)-Net in Base 4 — Upper bound on s

There is no (119, 260, 1458)-net in base 4, because

1 times m-reduction [i] would yield (119, 259, 1458)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 889428 329695 165376 203557 870040 364257 776070 467396 774441 230794 098982 493864 415676 263508 692103 978287 438526 580291 748228 063853 139630 146004 714702 998380 200733 165040 > 4²⁵⁹ [i]