MinT - Best Known (153−93, 153, s)-Nets in Base 8

Best Known (153−93, 153, s)-Nets in Base 8

(153−93, 153, 98)-Net over F₈ — Constructive and digital

Digital (60, 153, 98)-net over F₈, using

t-expansion [i] based on digital (37, 153, 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]

(153−93, 153, 144)-Net over F₈ — Digital

Digital (60, 153, 144)-net over F₈, using

t-expansion [i] based on digital (45, 153, 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]

(153−93, 153, 2449)-Net in Base 8 — Upper bound on s

There is no (60, 153, 2450)-net in base 8, because

1 times m-reduction [i] would yield (60, 152, 2450)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186382 155909 339480 388046 571994 625159 046929 388927 825362 847235 174431 012656 034140 834159 640095 602379 172734 941572 263960 196588 155258 485053 765792 > 8¹⁵² [i]