MinT - Best Known (153−115, 153, s)-Nets in Base 8

Best Known (153−115, 153, s)-Nets in Base 8

(153−115, 153, 98)-Net over F₈ — Constructive and digital

Digital (38, 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]

(153−115, 153, 129)-Net over F₈ — Digital

Digital (38, 153, 129)-net over F₈, using

net from sequence [i] based on digital (38, 128)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(153−115, 153, 771)-Net in Base 8 — Upper bound on s

There is no (38, 153, 772)-net in base 8, because

1 times m-reduction [i] would yield (38, 152, 772)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 188332 927324 147757 708579 428291 718939 480961 192546 178451 849506 449457 257061 269130 099012 763058 834548 732559 555345 073436 847903 778372 629321 129824 > 8¹⁵² [i]