MinT - Best Known (241−125, 241, s)-Nets in Base 4

Best Known (241−125, 241, s)-Nets in Base 4

(241−125, 241, 130)-Net over F₄ — Constructive and digital

Digital (116, 241, 130)-net over F₄, using

t-expansion [i] based on digital (105, 241, 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]

(241−125, 241, 168)-Net over F₄ — Digital

Digital (116, 241, 168)-net over F₄, using

t-expansion [i] based on digital (115, 241, 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]

(241−125, 241, 1657)-Net in Base 4 — Upper bound on s

There is no (116, 241, 1658)-net in base 4, because

1 times m-reduction [i] would yield (116, 240, 1658)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 214954 191856 512207 415605 275768 443263 759126 805344 205930 137880 130684 838560 647062 713220 209633 393342 915874 123113 185517 752656 671410 723777 461954 185440 > 4²⁴⁰ [i]