MinT - Best Known (98−73, 98, s)-Nets in Base 27

Best Known (98−73, 98, s)-Nets in Base 27

(98−73, 98, 114)-Net over F₂₇ — Constructive and digital

Digital (25, 98, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 98, 114)-net over F₂₇, using
- net from sequence [i] based on digital (23, 113)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 23 and N(F) ≥ 114, using
    - an explicitly constructive algebraic function field [i]

(98−73, 98, 208)-Net over F₂₇ — Digital

Digital (25, 98, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 98, 208)-net over F₂₇, using
- net from sequence [i] based on digital (24, 207)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208, using
    - an algebraic function field by Beelen and Pellikaan [i]

(98−73, 98, 3930)-Net in Base 27 — Upper bound on s

There is no (25, 98, 3931)-net in base 27, because

1 times m-reduction [i] would yield (25, 97, 3931)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 7 005915 506022 725938 670145 225331 782216 284196 467865 481837 771431 272879 646760 201974 394530 804254 463364 570993 604447 882938 022728 129654 841678 543929 > 27⁹⁷ [i]