MinT - Best Known (220−146, 220, s)-Nets in Base 4

Best Known (220−146, 220, s)-Nets in Base 4

(220−146, 220, 104)-Net over F₄ — Constructive and digital

Digital (74, 220, 104)-net over F₄, using

t-expansion [i] based on digital (73, 220, 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]

(220−146, 220, 112)-Net over F₄ — Digital

Digital (74, 220, 112)-net over F₄, using

t-expansion [i] based on digital (73, 220, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(220−146, 220, 550)-Net in Base 4 — Upper bound on s

There is no (74, 220, 551)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 918644 110255 988910 468732 823825 388783 338237 359254 858778 012765 026636 264959 691671 342931 613139 946247 838076 770802 444276 317298 979959 811392 > 4²²⁰ [i]