MinT - Best Known (118, 118+125, s)-Nets in Base 4

Best Known (118, 118+125, s)-Nets in Base 4

(118, 118+125, 130)-Net over F₄ — Constructive and digital

Digital (118, 243, 130)-net over F₄, using

t-expansion [i] based on digital (105, 243, 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]

(118, 118+125, 168)-Net over F₄ — Digital

Digital (118, 243, 168)-net over F₄, using

t-expansion [i] based on digital (115, 243, 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]

(118, 118+125, 1735)-Net in Base 4 — Upper bound on s

There is no (118, 243, 1736)-net in base 4, because

1 times m-reduction [i] would yield (118, 242, 1736)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51 232377 090061 853076 745073 970655 436285 571075 440487 712058 766817 163003 171810 060091 579163 941658 356878 901823 000537 854509 150795 418175 167968 721447 069448 > 4²⁴² [i]