MinT - Best Known (103, 103+108, s)-Nets in Base 4

Best Known (103, 103+108, s)-Nets in Base 4

(103, 103+108, 104)-Net over F₄ — Constructive and digital

Digital (103, 211, 104)-net over F₄, using

t-expansion [i] based on digital (73, 211, 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]

(103, 103+108, 144)-Net over F₄ — Digital

Digital (103, 211, 144)-net over F₄, using

t-expansion [i] based on digital (91, 211, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(103, 103+108, 1529)-Net in Base 4 — Upper bound on s

There is no (103, 211, 1530)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 961560 389065 833269 756361 823849 512483 351843 592483 339392 963607 670519 720401 605995 902291 597517 738468 066584 472916 086116 075154 859300 > 4²¹¹ [i]