MinT - Best Known (51, 148, s)-Nets in Base 8

Best Known (51, 148, s)-Nets in Base 8

(51, 148, 98)-Net over F₈ — Constructive and digital

Digital (51, 148, 98)-net over F₈, using

t-expansion [i] based on digital (37, 148, 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]

(51, 148, 144)-Net over F₈ — Digital

Digital (51, 148, 144)-net over F₈, using

t-expansion [i] based on digital (45, 148, 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]

(51, 148, 1530)-Net in Base 8 — Upper bound on s

There is no (51, 148, 1531)-net in base 8, because

1 times m-reduction [i] would yield (51, 147, 1531)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 708593 791562 949905 354407 490803 345841 874572 005429 581659 990750 276343 131828 313149 545542 753767 363162 303145 076220 968275 231529 214028 428805 > 8¹⁴⁷ [i]