MinT - Best Known (135−94, 135, s)-Nets in Base 5

Best Known (135−94, 135, s)-Nets in Base 5

(135−94, 135, 78)-Net over F₅ — Constructive and digital

Digital (41, 135, 78)-net over F₅, using

t-expansion [i] based on digital (38, 135, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(135−94, 135, 80)-Net over F₅ — Digital

Digital (41, 135, 80)-net over F₅, using

net from sequence [i] based on digital (41, 79)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 41 and N(F) ≥ 80, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(135−94, 135, 433)-Net in Base 5 — Upper bound on s

There is no (41, 135, 434)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 23975 455329 764230 276897 177477 506219 784050 736679 841698 942404 238259 446717 762383 554769 083804 977385 > 5¹³⁵ [i]