MinT - Best Known (142−94, 142, s)-Nets in Base 8

Best Known (142−94, 142, s)-Nets in Base 8

(142−94, 142, 98)-Net over F₈ — Constructive and digital

Digital (48, 142, 98)-net over F₈, using

t-expansion [i] based on digital (37, 142, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(142−94, 142, 144)-Net over F₈ — Digital

Digital (48, 142, 144)-net over F₈, using

t-expansion [i] based on digital (45, 142, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(142−94, 142, 1374)-Net in Base 8 — Upper bound on s

There is no (48, 142, 1375)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 174 109699 024214 668266 177984 663171 777493 467887 132620 591799 412569 598819 023084 175744 859347 181647 213668 201959 538112 408357 693029 514736 > 8¹⁴² [i]