MinT - Best Known (148−43, 148, s)-Nets in Base 5

Best Known (148−43, 148, s)-Nets in Base 5

(148−43, 148, 408)-Net over F₅ — Constructive and digital

Digital (105, 148, 408)-net over F₅, using

2 times m-reduction [i] based on digital (105, 150, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 75, 204)-net over F₂₅, using
  - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
      - a function field by GarcÃa and Quoos [i]

(148−43, 148, 1220)-Net over F₅ — Digital

Digital (105, 148, 1220)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−43, 148, 169505)-Net in Base 5 — Upper bound on s

There is no (105, 148, 169506)-net in base 5, because

1 times m-reduction [i] would yield (105, 147, 169506)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 605610 877251 513207 842555 618555 923354 852855 526537 717988 847205 265502 323378 933464 796159 036642 541851 679625 > 5¹⁴⁷ [i]