MinT - Best Known (103, 103+64, s)-Nets in Base 4

Best Known (103, 103+64, s)-Nets in Base 4

(103, 103+64, 130)-Net over F₄ — Constructive and digital

Digital (103, 167, 130)-net over F₄, using

27 times m-reduction [i] based on digital (103, 194, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 97, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(103, 103+64, 289)-Net over F₄ — Digital

Digital (103, 167, 289)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 103+64, 5886)-Net in Base 4 — Upper bound on s

There is no (103, 167, 5887)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35143 736247 134634 704598 778694 413196 294388 742495 198949 558722 255197 025496 831514 604056 049654 798587 370105 > 4¹⁶⁷ [i]