MinT - Best Known (202−124, 202, s)-Nets in Base 4

Best Known (202−124, 202, s)-Nets in Base 4

(202−124, 202, 104)-Net over F₄ — Constructive and digital

Digital (78, 202, 104)-net over F₄, using

t-expansion [i] based on digital (73, 202, 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]

(202−124, 202, 112)-Net over F₄ — Digital

Digital (78, 202, 112)-net over F₄, using

t-expansion [i] based on digital (73, 202, 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]

(202−124, 202, 680)-Net in Base 4 — Upper bound on s

There is no (78, 202, 681)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43 737509 875886 183395 166587 857245 307387 266762 357424 654940 541718 198399 348334 882618 819728 048224 934749 013472 225396 710555 774400 > 4²⁰² [i]