MinT - Best Known (102−31, 102, s)-Nets in Base 4

Best Known (102−31, 102, s)-Nets in Base 4

(102−31, 102, 312)-Net over F₄ — Constructive and digital

Digital (71, 102, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 34, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(102−31, 102, 462)-Net over F₄ — Digital

Digital (71, 102, 462)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−31, 102, 24227)-Net in Base 4 — Upper bound on s

There is no (71, 102, 24228)-net in base 4, because

1 times m-reduction [i] would yield (71, 101, 24228)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 431434 061424 979944 217332 772950 922689 898119 949688 297096 218024 > 4¹⁰¹ [i]