MinT - Best Known (37, 158, s)-Nets in Base 8

Best Known (37, 158, s)-Nets in Base 8

(37, 158, 98)-Net over F₈ — Constructive and digital

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]

(37, 158, 121)-Net over F₈ — Digital

Digital (37, 158, 121)-net over F₈, using

net from sequence [i] based on digital (37, 120)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 121, using
  - a curve from the manYPoints database [i]

(37, 158, 726)-Net in Base 8 — Upper bound on s

There is no (37, 158, 727)-net in base 8, because

1 times m-reduction [i] would yield (37, 157, 727)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6147 030597 036936 807237 272937 841856 142789 998958 513603 351465 485585 623160 680692 737778 975836 298236 484849 296517 971195 165989 969665 546636 905454 833464 > 8¹⁵⁷ [i]