MinT - Best Known (148−112, 148, s)-Nets in Base 8

Best Known (148−112, 148, s)-Nets in Base 8

(148−112, 148, 65)-Net over F₈ — Constructive and digital

Digital (36, 148, 65)-net over F₈, using

t-expansion [i] based on digital (14, 148, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(148−112, 148, 112)-Net over F₈ — Digital

Digital (36, 148, 112)-net over F₈, using

t-expansion [i] based on digital (35, 148, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(148−112, 148, 720)-Net in Base 8 — Upper bound on s

There is no (36, 148, 721)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 46 879604 855550 257007 620113 434365 482261 388736 334110 198723 340436 436331 003548 471700 651393 300813 007268 167154 342548 263043 019876 634318 752856 > 8¹⁴⁸ [i]