MinT - Best Known (95, 95+148, s)-Nets in Base 4

Best Known (95, 95+148, s)-Nets in Base 4

(95, 95+148, 104)-Net over F₄ — Constructive and digital

Digital (95, 243, 104)-net over F₄, using

t-expansion [i] based on digital (73, 243, 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]

(95, 95+148, 144)-Net over F₄ — Digital

Digital (95, 243, 144)-net over F₄, using

t-expansion [i] based on digital (91, 243, 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]

(95, 95+148, 837)-Net in Base 4 — Upper bound on s

There is no (95, 243, 838)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 207 332228 155983 876072 651171 591197 433207 146180 968218 043055 963437 651799 962748 242435 938629 882476 292649 237682 105697 472373 535481 727432 687431 947829 075520 > 4²⁴³ [i]