MinT - Best Known (244−57, 244, s)-Nets in Base 4

Best Known (244−57, 244, s)-Nets in Base 4

(244−57, 244, 1044)-Net over F₄ — Constructive and digital

Digital (187, 244, 1044)-net over F₄, using

trace code for nets [i] based on digital (4, 61, 261)-net over F₂₅₆, using
- net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(244−57, 244, 3067)-Net over F₄ — Digital

Digital (187, 244, 3067)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−57, 244, 632249)-Net in Base 4 — Upper bound on s

There is no (187, 244, 632250)-net in base 4, because

1 times m-reduction [i] would yield (187, 243, 632250)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 199 793300 045903 154656 107498 419141 269576 161816 226521 116673 380755 810472 795031 362011 584897 607869 778584 988833 347282 673344 176759 602824 293959 410518 527096 > 4²⁴³ [i]