MinT - Best Known (48, 48+121, s)-Nets in Base 8

Best Known (48, 48+121, s)-Nets in Base 8

(48, 48+121, 98)-Net over F₈ — Constructive and digital

Digital (48, 169, 98)-net over F₈, using

t-expansion [i] based on digital (37, 169, 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]

(48, 48+121, 144)-Net over F₈ — Digital

Digital (48, 169, 144)-net over F₈, using

t-expansion [i] based on digital (45, 169, 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]

(48, 48+121, 1081)-Net in Base 8 — Upper bound on s

There is no (48, 169, 1082)-net in base 8, because

1 times m-reduction [i] would yield (48, 168, 1082)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 53 883828 384371 584922 591506 966033 560385 470956 073189 081554 813410 686435 118461 474974 773046 155187 536746 928694 892304 957600 441016 053543 407986 657457 163545 204992 > 8¹⁶⁸ [i]