MinT - Best Known (75, 242, s)-Nets in Base 4

Best Known (75, 242, s)-Nets in Base 4

(75, 242, 104)-Net over F₄ — Constructive and digital

Digital (75, 242, 104)-net over F₄, using

t-expansion [i] based on digital (73, 242, 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]

(75, 242, 112)-Net over F₄ — Digital

Digital (75, 242, 112)-net over F₄, using

t-expansion [i] based on digital (73, 242, 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]

(75, 242, 526)-Net in Base 4 — Upper bound on s

There is no (75, 242, 527)-net in base 4, because

1 times m-reduction [i] would yield (75, 241, 527)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 14 344306 659321 859655 818289 540490 090964 797153 134288 312154 684687 317217 843817 341251 441472 445809 981409 322444 301414 017619 904842 874509 599029 335507 510016 > 4²⁴¹ [i]