MinT - Best Known (118−42, 118, s)-Nets in Base 5

Best Known (118−42, 118, s)-Nets in Base 5

(118−42, 118, 252)-Net over F₅ — Constructive and digital

Digital (76, 118, 252)-net over F₅, using

14 times m-reduction [i] based on digital (76, 132, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 66, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(118−42, 118, 413)-Net over F₅ — Digital

Digital (76, 118, 413)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(118−42, 118, 18349)-Net in Base 5 — Upper bound on s

There is no (76, 118, 18350)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 30119 473371 515502 664699 441663 917425 590399 488180 347055 124555 412547 824312 220176 217401 > 5¹¹⁸ [i]