MinT - Best Known (149−103, 149, s)-Nets in Base 8

Best Known (149−103, 149, s)-Nets in Base 8

(149−103, 149, 98)-Net over F₈ — Constructive and digital

Digital (46, 149, 98)-net over F₈, using

t-expansion [i] based on digital (37, 149, 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]

(149−103, 149, 144)-Net over F₈ — Digital

Digital (46, 149, 144)-net over F₈, using

t-expansion [i] based on digital (45, 149, 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]

(149−103, 149, 1152)-Net in Base 8 — Upper bound on s

There is no (46, 149, 1153)-net in base 8, because

1 times m-reduction [i] would yield (46, 148, 1153)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 46 708501 538012 274132 455139 908506 237429 418284 807918 102014 837733 629998 921554 672227 339528 414012 080864 807872 177787 927755 613646 400438 332032 > 8¹⁴⁸ [i]