MinT - Best Known (87, 227, s)-Nets in Base 4

Best Known (87, 227, s)-Nets in Base 4

(87, 227, 104)-Net over F₄ — Constructive and digital

Digital (87, 227, 104)-net over F₄, using

t-expansion [i] based on digital (73, 227, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(87, 227, 129)-Net over F₄ — Digital

Digital (87, 227, 129)-net over F₄, using

t-expansion [i] based on digital (81, 227, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(87, 227, 747)-Net in Base 4 — Upper bound on s

There is no (87, 227, 748)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50059 586976 983652 000758 974373 123451 129516 985687 840132 365074 946475 919576 890500 220727 447791 252156 032578 699072 013426 531358 847579 258755 666006 > 4²²⁷ [i]