MinT - Best Known (140−51, 140, s)-Nets in Base 5

Best Known (140−51, 140, s)-Nets in Base 5

(140−51, 140, 296)-Net over F₅ — Constructive and digital

Digital (89, 140, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 70, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(140−51, 140, 431)-Net over F₅ — Digital

Digital (89, 140, 431)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−51, 140, 19562)-Net in Base 5 — Upper bound on s

There is no (89, 140, 19563)-net in base 5, because

1 times m-reduction [i] would yield (89, 139, 19563)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 14 350301 332646 145604 646945 896085 033565 483275 986540 060771 147131 235116 001291 546315 795739 442442 002253 > 5¹³⁹ [i]