MinT - Best Known (208−133, 208, s)-Nets in Base 4

Best Known (208−133, 208, s)-Nets in Base 4

(208−133, 208, 104)-Net over F₄ — Constructive and digital

Digital (75, 208, 104)-net over F₄, using

t-expansion [i] based on digital (73, 208, 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]

(208−133, 208, 112)-Net over F₄ — Digital

Digital (75, 208, 112)-net over F₄, using

t-expansion [i] based on digital (73, 208, 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]

(208−133, 208, 602)-Net in Base 4 — Upper bound on s

There is no (75, 208, 603)-net in base 4, because

1 times m-reduction [i] would yield (75, 207, 603)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46016 061916 372658 969415 512061 559576 148261 685967 072034 477040 265094 331391 508959 881677 576898 153842 015789 757474 776664 224487 827305 > 4²⁰⁷ [i]