MinT - Best Known (260−160, 260, s)-Nets in Base 4

Best Known (260−160, 260, s)-Nets in Base 4

(260−160, 260, 104)-Net over F₄ — Constructive and digital

Digital (100, 260, 104)-net over F₄, using

t-expansion [i] based on digital (73, 260, 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]

(260−160, 260, 144)-Net over F₄ — Digital

Digital (100, 260, 144)-net over F₄, using

t-expansion [i] based on digital (91, 260, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(260−160, 260, 858)-Net in Base 4 — Upper bound on s

There is no (100, 260, 859)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 524175 778493 112574 316977 541758 740399 096867 710421 576445 990600 220809 429911 082365 772170 323741 165979 168677 489999 090680 661284 684876 789947 717340 923768 422398 974427 > 4²⁶⁰ [i]