MinT - Best Known (98, 98+38, s)-Nets in Base 5

Best Known (98, 98+38, s)-Nets in Base 5

(98, 98+38, 408)-Net over F₅ — Constructive and digital

Digital (98, 136, 408)-net over F₅, using

trace code for nets [i] based on digital (30, 68, 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]

(98, 98+38, 1377)-Net over F₅ — Digital

Digital (98, 136, 1377)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+38, 199654)-Net in Base 5 — Upper bound on s

There is no (98, 136, 199655)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 114798 729783 634794 300399 319491 583843 618880 860077 112238 843701 746757 866701 004022 092694 980744 183765 > 5¹³⁶ [i]