MinT - Best Known (9, 9+26, s)-Nets in Base 4

Best Known (9, 9+26, s)-Nets in Base 4

(9, 9+26, 22)-Net over F₄ — Constructive and digital

Digital (9, 35, 22)-net over F₄, using

net from sequence [i] based on digital (9, 21)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 22, using
  - an explicitly constructive algebraic function field [i]

(9, 9+26, 26)-Net over F₄ — Digital

Digital (9, 35, 26)-net over F₄, using

net from sequence [i] based on digital (9, 25)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 26, using
  - Drinfeld modules of rank 1 [i]

(9, 9+26, 59)-Net in Base 4 — Upper bound on s

There is no (9, 35, 60)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4³⁵, 60, S₄, 26), but
- the linear programming bound shows that MÂ â‰¥ 127 021609 043192 292437 843389 367812 358144 / 97271 284126 260933 > 4³⁵ [i]