MinT - Best Known (98, 98+93, s)-Nets in Base 3

Best Known (98, 98+93, s)-Nets in Base 3

(98, 98+93, 72)-Net over F₃ — Constructive and digital

Digital (98, 191, 72)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 72, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using
      - an explicitly constructive algebraic function field [i]
2. digital (26, 119, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃ (see above)

(98, 98+93, 104)-Net over F₃ — Digital

Digital (98, 191, 104)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+93, 796)-Net in Base 3 — Upper bound on s

There is no (98, 191, 797)-net in base 3, because

1 times m-reduction [i] would yield (98, 190, 797)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 564353 859162 833340 856141 808551 362170 580221 280447 314161 625640 103243 342275 972225 386368 915025 > 3¹⁹⁰ [i]