MinT - Best Known (220−142, 220, s)-Nets in Base 4

Best Known (220−142, 220, s)-Nets in Base 4

(220−142, 220, 104)-Net over F₄ — Constructive and digital

Digital (78, 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]

(220−142, 220, 112)-Net over F₄ — Digital

Digital (78, 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]

(220−142, 220, 610)-Net in Base 4 — Upper bound on s

There is no (78, 220, 611)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 127444 500604 088539 238478 027169 781988 570377 637590 626656 490006 573342 154938 404330 347581 718807 901333 170436 861638 801289 738203 246349 068224 > 4²²⁰ [i]