MinT - Best Known (259−134, 259, s)-Nets in Base 4

Best Known (259−134, 259, s)-Nets in Base 4

(259−134, 259, 130)-Net over F₄ — Constructive and digital

Digital (125, 259, 130)-net over F₄, using

t-expansion [i] based on digital (105, 259, 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]

(259−134, 259, 176)-Net over F₄ — Digital

Digital (125, 259, 176)-net over F₄, using

net from sequence [i] based on digital (125, 175)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 125 and N(F) ≥ 176, using
  - Drinfeld modules of rank 1 [i]

(259−134, 259, 1771)-Net in Base 4 — Upper bound on s

There is no (125, 259, 1772)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 864834 022950 956265 885894 233699 338222 597540 055832 564554 310286 763775 709606 869100 476301 629008 103737 195288 643101 149067 708961 534630 931893 559266 699183 547593 399235 > 4²⁵⁹ [i]