MinT - Best Known (202−127, 202, s)-Nets in Base 4

Best Known (202−127, 202, s)-Nets in Base 4

(202−127, 202, 104)-Net over F₄ — Constructive and digital

Digital (75, 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]

(202−127, 202, 112)-Net over F₄ — Digital

Digital (75, 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]

(202−127, 202, 624)-Net in Base 4 — Upper bound on s

There is no (75, 202, 625)-net in base 4, because

1 times m-reduction [i] would yield (75, 201, 625)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 691288 184661 377624 037660 788228 502054 887322 726391 932948 776819 539300 269886 589663 031933 887264 744539 114734 520089 062581 296576 > 4²⁰¹ [i]