MinT - Best Known (230−118, 230, s)-Nets in Base 4

Best Known (230−118, 230, s)-Nets in Base 4

(230−118, 230, 130)-Net over F₄ — Constructive and digital

Digital (112, 230, 130)-net over F₄, using

t-expansion [i] based on digital (105, 230, 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]

(230−118, 230, 165)-Net over F₄ — Digital

Digital (112, 230, 165)-net over F₄, using

t-expansion [i] based on digital (109, 230, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(230−118, 230, 1643)-Net in Base 4 — Upper bound on s

There is no (112, 230, 1644)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 061033 178719 101509 532976 068524 486127 826965 763154 153359 489883 660002 690788 574292 432846 051465 737366 144330 370908 257560 922871 056546 570799 875292 > 4²³⁰ [i]