MinT - Best Known (61, 61+97, s)-Nets in Base 8

Best Known (61, 61+97, s)-Nets in Base 8

(61, 61+97, 98)-Net over F₈ — Constructive and digital

Digital (61, 158, 98)-net over F₈, using

t-expansion [i] based on digital (37, 158, 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]

(61, 61+97, 144)-Net over F₈ — Digital

Digital (61, 158, 144)-net over F₈, using

t-expansion [i] based on digital (45, 158, 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]

(61, 61+97, 2377)-Net in Base 8 — Upper bound on s

There is no (61, 158, 2378)-net in base 8, because

1 times m-reduction [i] would yield (61, 157, 2378)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6200 095519 939640 168951 061861 931982 901929 729996 232380 871074 756160 133190 366190 763664 063049 597731 699331 657984 698771 250218 423372 181845 955895 510068 > 8¹⁵⁷ [i]