MinT - Best Known (98−68, 98, s)-Nets in Base 2

Best Known (98−68, 98, s)-Nets in Base 2

(98−68, 98, 21)-Net over F₂ — Constructive and digital

Digital (30, 98, 21)-net over F₂, using

t-expansion [i] based on digital (21, 98, 21)-net over F₂, using
- net from sequence [i] based on digital (21, 20)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(98−68, 98, 25)-Net over F₂ — Digital

Digital (30, 98, 25)-net over F₂, using

t-expansion [i] based on digital (28, 98, 25)-net over F₂, using
- net from sequence [i] based on digital (28, 24)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 28 and N(F) ≥ 25, using
    - a curve from the manYPoints database [i]

(98−68, 98, 47)-Net in Base 2 — Upper bound on s

There is no (30, 98, 48)-net in base 2, because

8 times m-reduction [i] would yield (30, 90, 48)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁹⁰, 48, S₂, 2, 60), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 79228 162514 264337 593543 950336 / 61 > 2⁹⁰ [i]