MinT - Best Known (35, 35+45, s)-Nets in Base 8

Best Known (35, 35+45, s)-Nets in Base 8

(35, 35+45, 70)-Net over F₈ — Constructive and digital

Digital (35, 80, 70)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (4, 26, 25)-net over F₈, using
  - net from sequence [i] based on digital (4, 24)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
      - a function field by SÃ©mirat [i]
2. digital (9, 54, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(35, 35+45, 112)-Net over F₈ — Digital

Digital (35, 80, 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]

(35, 35+45, 2249)-Net in Base 8 — Upper bound on s

There is no (35, 80, 2250)-net in base 8, because

1 times m-reduction [i] would yield (35, 79, 2250)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 222360 004010 525745 937405 693442 541494 638479 056066 776639 245653 410248 000976 > 8⁷⁹ [i]