MinT - Best Known (253−53, 253, s)-Nets in Base 4

Best Known (253−53, 253, s)-Nets in Base 4

(253−53, 253, 1539)-Net over F₄ — Constructive and digital

Digital (200, 253, 1539)-net over F₄, using

5 times m-reduction [i] based on digital (200, 258, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 86, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(253−53, 253, 5754)-Net over F₄ — Digital

Digital (200, 253, 5754)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(253−53, 253, 2407235)-Net in Base 4 — Upper bound on s

There is no (200, 253, 2407236)-net in base 4, because

1 times m-reduction [i] would yield (200, 252, 2407236)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 374307 285346 474880 138979 470619 391869 704120 529987 066548 883609 851217 834890 705073 309647 526102 650132 698560 094679 524582 051608 568375 248159 718883 605427 590104 > 4²⁵² [i]